Question

Adya and Ashley complete a work separately in 20 and 25 days respectively. After 10 days of their working together, they both left then Amber came and completed the remaining work in 3 days. If Amber alone would do the work, calculate how many days he would take to complete the work.?​

Answer 1

`\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}`

Number of days Adya took to complete the work = 20

Work done by Adya in 1 day =
`(1)/(20)`

Number of days Ashley took to complete the work = 25

Work done by Ashley in 1 day =
`(1)/(25)`

So,

Total work by Adya & Ashley in 1 day =

`(1)/(20) + (1)/(20) \\ = (5 + 4)/(100) \\ = (9)/(100)`

•°• Their total work in 10 days =

`(9 * 10)/(100) \\ = (90)/(100) \\ = (9)/(10)`

Now,

The work left to be completed =

`1 - (9)/(10) \\ = (10)/(10) - (9)/(10) \\ = (1)/(10)`

From this we know that,

Amber completes
`(1)/(10)` of the work in 3 days.

So,

Time taken by Amber to complete the whole work =

`3 * 10 \\ = 30 \: \: days`

↦ If Amber alone would do the whole work, he would take
`\boxed{30 \ \ days}` to complete it.

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